Shells, of electrons

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

Cadmium is a member of Group 12 (Zn, Cd, Hg) of the Periodic Table, having a filled d shell of electrons which dictates the usual valence state of... 

Every chemist knows that atomic nuclei are surrounded by shells of electrons, which, when completed, contain 2 (inner shell), 8, 8, 18,. . . electrons, this being the explanation of periodicity in chemical properties. For reasons that will appear, these may be called (in the same order) K, L, M, N,. . . electrons on the basis of conclusive x-ray evidence. 

The first set of screening constants was obtained from the discussion of the motion of an electron in the field of the nucleus and its surrounding electron shells, idealized as electrical charges uniformly distributed over spherical surfaces of suitably chosen radii. This idealization of electron shells was first used by Schrodinger3), and later by Heisenberg4) and Unsold5), who pointed out that it is justified to a considerable extent by the quantum mechanics. The radius of a shell of electrons with principal quantum number nt is taken as... 

A formal charge is a charge associated with an atom that does not exhibit the expected number of valence electrons. When calculating the formal charge on an atom, we first need to know the number of valence electrons the atom is supposed to have. We can get this number by inspecting the periodic table, since each column of the periodic table indicates the number of expected valence electrons (valence electrons are the electrons in the valence shell, or the outermost shell of electrons— you probably remember this from high school chemistry). For example, carbon is in Column 4A, and therefore has four valence electrons. Now you know how to determine how many electrons the atom is supposed to have. 

Studies of the electron distributions around outer atoms consistently show that hydrogen is always associated with two electrons (one pair). All other outer atoms always have eight electrons (four pairs). The reason for this regularity is that each atom in a molecule is most stable when its valence shell of electrons is complete. For hydrogen, this requires a single pair of electrons, enough to make full use of the hydrogen 1 S orbital. Any other atom needs four pairs of electrons, the maximum number that can be accommodated by an .S p valence shell. Details of these features can be traced to the properties of atoms (Chapter 8) and are discussed further in Chapter 10. 

Suppose we want to write the electron configuration of scandium (atomic number 21). We can rewrite the first 12 electrons that we wrote above for magnesium, and then just keep going. As we added electrons, we filled the first shell of electrons first, then the second shell. When we are filling the third shell, we have to ask if the electrons with n = 3 and / = 2 will enter before the n = 4 and 1 = 0 electrons. Since (n + /) for the former is 5 and that for the latter is 4, we must add the two electrons with n = 4 and / = 0 before the last 10 electrons with n = 3 and / = 2. In this discussion, the values of m and s tell us how many electrons can have the same set of n and / values, but do not matter as to which come first. 

It must be emphasized that the octet rule does not describe the electron configuration of all compounds. The very existence of any compounds of the noble gases is evidence that the octet rule does not apply in all cases. Other examples of compounds that do not obey the octet rule are BF,. PF5, and SF6. But the octet rule does summarize, systematize, and explain the bonding in so many compounds that it is well worth learning and understanding. Compounds in which atoms attain the configuration of helium (the duet) are considered to obey the octet rule, despite the fact that they achieve only the duet characteristic of the complete first shell of electrons. 

For the conduction electrons, it is reasonable to consider that the inner-shell electrons are all localized on individual nuclei, in wave functions very much like those they occupy in the free atoms. The potential V should then include the potential due to the positively charged ions, each consisting of a nucleus plus filled inner shells of electrons, and the self-consistent potential (coulomb plus exchange) of the conduction electrons. However, the potential of an ion core must include the effect of exchange or antisymmetry with the inner-shell or core electrons, which means that the conduction-band wave functions must be orthogonal to the core-electron wave functions. This is the basis of the orthogonalized-plane-wave method, which has been successfully used to calculate band structures for many metals.41... 

Electrophiles seek the extra electrons that will give them a stable valence shell of electrons. 

Structures in which all of the atoms have a complete valence shell of electrons are especially stable and make large contributions to the hybrid. 

The electrons in the outermost shell of electrons surrounding an atomic nucleus, the number of which determines the valency of the atom. 

In general, the ionization potential decreases for the atoms in a given group going down in the group. For example, Li > Na > K > Rb > Cs and F > Cl > Br > I. The outer electrons are farther from the nucleus for the larger atoms, and there are more filled shells of electrons between the nucleus and the outermost electron. 

As was described earlier in this chapter, the model of the atom consists of shells of electrons surrounding the nucleus, which contains protons and, except for the isotope 1H, a certain number of neutrons. 

Because of their having larger sizes and more filled shells of electrons between the outer shell and the nucleus, the ionization energies of second- and third-row metals are lower than those of first-row metals. Consequently, it is easier for the heavier metals to achieve higher oxidation states, which also favors higher coordination numbers. In general, there is also a greater tendency of the heavier metals... 

A further simplication often used in density-functional calculations is the use of pseudopotentials. Most properties of molecules and solids are indeed determined by the valence electrons, i.e., those electrons in outer shells that take part in the bonding between atoms. The core electrons can be removed from the problem by representing the ionic core (i.e., nucleus plus inner shells of electrons) by a pseudopotential. State-of-the-art calculations employ nonlocal, norm-conserving pseudopotentials that are generated from atomic calculations and do not contain any fitting to experiment (Hamann et al., 1979). Such calculations can therefore be called ab initio, or first-principles. ... 

An unstable, low n p ratio may also be adjusted by the capture of an orbital electron, which would naturally involve the nearest shell, K-shell, of electrons... 

We have not mentioned open shells of electrons in our general considerations but then we have not specifically mentioned closed shells either. Certainly our examples are all closed shell but this choice simply reflects our main area of interest valence theory. The derivations and considerations of constraints in the opening sections are independent of the numbers of electrons involved in the system and, in particular, are independent of the magnetic properties of the molecules concerned simply because the spin variable does not occur in our approximate Hamiltonian. Nevertheless, it is traditional to treat open and closed shells of electrons by separate techniques and it is of some interest to investigate the consequences of this dichotomy. The independent-electron model (UHF - no symmetry constraints) is the simplest one to investigate we give below an abbreviated discussion. 

Lewis appropriated Bohr s new atom to try to unify the physical and chemical atom. If the Bohr-Sommerfeld orbits are in fixed positions and orientations, "they may be used as the building stones of an atom which has an essentially static character." 17 Bohr s dynamic theory works for the chemist, Lewis wrote, if the "average" position of an electron in a Bohr-Sommerfeld orbit is taken to correspond to the fixed position of the electron in Lewis s static chemical model. The outermost shell of electrons constitutes the "valence" electrons, and the remaining electrons constitute the "kernel." 18... 

The o-scales in Table 1 were derived for molecules with a closed shell of electrons and not for free radicals. However, the concept of captodative... 

There are seven possible shells or energy levels for electrons surrounding the nucleus at a relatively great distance. The hghtest atoms have only one shell, which is the innermost shell closest to the nucleus. Other atoms have multiple shells, and the largest and heaviest atoms have all seven shells of electrons. AH the electrons in a particular shell have the same energy. The electrons... 

Nickel is a transition metal in group Vin of the Periodic Table following iron and cobalt (Cotton and Wilkinson 1980). Its outer shell of electrons has a 4s 3d configuration. While nickel can exist in oxidation states -1, 0, +2, +3, and +4, its only important oxidation state is nickel(+2) under normal environmental conditions. 

It is imperative to use CASSCF wave functions for singlet diradicals and other open-shell molecules for which a single configuration provides an inadequate description of the wave function. However, perhaps surprisingly, CASSCF calculations often perform rather poorly in calculations on molecules and TSs with closed shells of electrons, if the active electrons are delocalized. An example is... 

---